Step |
Hyp |
Ref |
Expression |
1 |
|
ghmgrp.f |
|
2 |
|
ghmgrp.x |
|
3 |
|
ghmgrp.y |
|
4 |
|
ghmgrp.p |
|
5 |
|
ghmgrp.q |
|
6 |
|
ghmgrp.1 |
|
7 |
|
mhmmnd.3 |
|
8 |
|
simpllr |
|
9 |
|
simpr |
|
10 |
8 9
|
oveq12d |
|
11 |
|
simp-5l |
|
12 |
11 1
|
syl3an1 |
|
13 |
|
simp-4r |
|
14 |
|
simplr |
|
15 |
12 13 14
|
mhmlem |
|
16 |
|
fof |
|
17 |
6 16
|
syl |
|
18 |
17
|
ad5antr |
|
19 |
7
|
ad5antr |
|
20 |
2 4
|
mndcl |
|
21 |
19 13 14 20
|
syl3anc |
|
22 |
18 21
|
ffvelrnd |
|
23 |
15 22
|
eqeltrrd |
|
24 |
10 23
|
eqeltrrd |
|
25 |
|
simpr |
|
26 |
|
foelrni |
|
27 |
6 25 26
|
syl2an |
|
28 |
27
|
ad2antrr |
|
29 |
24 28
|
r19.29a |
|
30 |
|
simpl |
|
31 |
|
foelrni |
|
32 |
6 30 31
|
syl2an |
|
33 |
29 32
|
r19.29a |
|
34 |
|
simpll |
|
35 |
|
simplrl |
|
36 |
|
simplrr |
|
37 |
|
simpr |
|
38 |
7
|
ad2antrr |
|
39 |
38
|
ad5antr |
|
40 |
|
simp-6r |
|
41 |
|
simp-4r |
|
42 |
|
simplr |
|
43 |
2 4
|
mndass |
|
44 |
39 40 41 42 43
|
syl13anc |
|
45 |
44
|
fveq2d |
|
46 |
|
simp-7l |
|
47 |
46 1
|
syl3an1 |
|
48 |
39 40 41 20
|
syl3anc |
|
49 |
47 48 42
|
mhmlem |
|
50 |
2 4
|
mndcl |
|
51 |
39 41 42 50
|
syl3anc |
|
52 |
47 40 51
|
mhmlem |
|
53 |
45 49 52
|
3eqtr3d |
|
54 |
|
simp1 |
|
55 |
54 1
|
syl3an1 |
|
56 |
|
simp2 |
|
57 |
|
simp3 |
|
58 |
55 56 57
|
mhmlem |
|
59 |
46 40 41 58
|
syl3anc |
|
60 |
59
|
oveq1d |
|
61 |
47 41 42
|
mhmlem |
|
62 |
61
|
oveq2d |
|
63 |
53 60 62
|
3eqtr3d |
|
64 |
|
simp-5r |
|
65 |
|
simpllr |
|
66 |
64 65
|
oveq12d |
|
67 |
|
simpr |
|
68 |
66 67
|
oveq12d |
|
69 |
65 67
|
oveq12d |
|
70 |
64 69
|
oveq12d |
|
71 |
63 68 70
|
3eqtr3d |
|
72 |
|
foelrni |
|
73 |
6 72
|
sylan |
|
74 |
73
|
3ad2antr3 |
|
75 |
74
|
ad4antr |
|
76 |
71 75
|
r19.29a |
|
77 |
27
|
3adantr3 |
|
78 |
77
|
ad2antrr |
|
79 |
76 78
|
r19.29a |
|
80 |
32
|
3adantr3 |
|
81 |
79 80
|
r19.29a |
|
82 |
34 35 36 37 81
|
syl13anc |
|
83 |
82
|
ralrimiva |
|
84 |
33 83
|
jca |
|
85 |
84
|
ralrimivva |
|
86 |
|
eqid |
|
87 |
2 86
|
mndidcl |
|
88 |
7 87
|
syl |
|
89 |
17 88
|
ffvelrnd |
|
90 |
|
simplll |
|
91 |
90 1
|
syl3an1 |
|
92 |
7
|
ad3antrrr |
|
93 |
92 87
|
syl |
|
94 |
|
simplr |
|
95 |
91 93 94
|
mhmlem |
|
96 |
2 4 86
|
mndlid |
|
97 |
92 94 96
|
syl2anc |
|
98 |
97
|
fveq2d |
|
99 |
95 98
|
eqtr3d |
|
100 |
|
simpr |
|
101 |
100
|
oveq2d |
|
102 |
99 101 100
|
3eqtr3d |
|
103 |
91 94 93
|
mhmlem |
|
104 |
2 4 86
|
mndrid |
|
105 |
92 94 104
|
syl2anc |
|
106 |
105
|
fveq2d |
|
107 |
103 106
|
eqtr3d |
|
108 |
100
|
oveq1d |
|
109 |
107 108 100
|
3eqtr3d |
|
110 |
102 109
|
jca |
|
111 |
6 31
|
sylan |
|
112 |
110 111
|
r19.29a |
|
113 |
112
|
ralrimiva |
|
114 |
|
oveq1 |
|
115 |
114
|
eqeq1d |
|
116 |
115
|
ovanraleqv |
|
117 |
116
|
rspcev |
|
118 |
89 113 117
|
syl2anc |
|
119 |
3 5
|
ismnd |
|
120 |
85 118 119
|
sylanbrc |
|